We construct phantom energy models with the equation of state parameter w which is less than −1, w < −1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ("phantom energy" without "Big Rip" singularity) and (ii) energy density tends to constant value with time ("cosmological constant" with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

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A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding Friedmann Robertson Walker spacetimesWe present an interesting connection between Einstein-Friedmann equations for the models of universe filled with scalar field and the special form of Abel equation of the first kind. This connection works in both ways: first, we show how, knowing the general solution of the Abel equation ͑corresponding to the given scalar field potential͒, one can obtain the general solution of the Friedman equation ͑and use the former for studying such problems as the existence of inflation with exit for particular models͒. On the other hand, one can invert the procedure and construct the Bäcklund autotransformations for the Abel equation.

We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspond to symmetry breaking and all restored potentials are similar either to the Phi**4-model or to the sineGordon model.